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On Asymptotic Dimension of Groups Acting on Trees

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Abstract

We prove the following.

THEOREM. Let π be the fundamental group of a finite graph of groups with finitely generated vertex groups G v having asdim G v ≤n for all vertices v. Then asdim π≤n+1.

This gives the best possible estimate for the asymptotic dimension of an HNN extension and the amalgamated product.

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Authors and Affiliations

  1. Department of Mathematics, University of Louisville, 328 Natural Sciences Building, Louisville, KY, 40292, U.S.A

    G. Bell

  2. Department of Mathematics, University of Florida, PO Box 118105, 358 Little Hall, Gainesville, FL, 32611-8105, U.S.A

    A. Dranishnikov

Authors
  1. G. Bell
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  2. A. Dranishnikov
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Bell, G., Dranishnikov, A. On Asymptotic Dimension of Groups Acting on Trees. Geometriae Dedicata 103, 89–101 (2004). https://doi.org/10.1023/B:GEOM.0000013843.53884.77

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  • DOI: https://doi.org/10.1023/B:GEOM.0000013843.53884.77

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